Pith Number

pith:QJIPKZ3U

pith:2007:QJIPKZ3UDZYABEGI3IRDFECD34

not attested not anchored not stored refs pending

Strong invariance principles for dependent random variables

Wei Biao Wu

arxiv:0711.3674 v1 · 2007-11-23 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJIPKZ3UDZYABEGI3IRDFECD34}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:09:04.524484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8250f567741e700090c8da22329043df3d4c3cc97ec1f2aea3109c81058b6d64

Aliases

arxiv: 0711.3674 · arxiv_version: 0711.3674v1 · doi: 10.48550/arxiv.0711.3674 · pith_short_12: QJIPKZ3UDZYA · pith_short_16: QJIPKZ3UDZYABEGI · pith_short_8: QJIPKZ3U

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QJIPKZ3UDZYABEGI3IRDFECD34 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8250f567741e700090c8da22329043df3d4c3cc97ec1f2aea3109c81058b6d64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7df1fd06d1afeaa3a3c5b0a82b987f7629e9e2ec7414c3fa81c4992e0482d129",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-11-23T07:44:05Z",
    "title_canon_sha256": "f87570829d92228a100933cafccfb48038490ce63a7f07886a97932e4d216f07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.3674",
    "kind": "arxiv",
    "version": 1
  }
}